CS 128/ES 228 - Lecture 13b 1

Surface Analysis

CS 128/ES 228 - Lecture 13b 2

How do we display a map with “elevation”?

Chloropleth map

Contour map

Surface map

CS 128/ES 228 - Lecture 13b 3

Chloropleth maps Show areas of equal “elevation” in a

uniform manner

Are usually “exact” approximations (through aggregation)

Subject to classification issues

Often intimately connected to queries

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Simple uses of chloropleths

Ordinal

Population

Per capita income

Crop yield

Categorical

Soil type

Political party control

Primary industry

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Display issues for chloropleths Classification

Type

Number of intervals

Colors

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To dissolve or not to dissolve: That is the question

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More complex queries using chloropleths Time series data

Population change % of land in agricultural use

Computation driven Total spending power = Average income x population Average wheat yield = Total yield / Number of farms

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Basic model for “computed chloropleths” Use a query to create new attribute

data

Set the display to use that new data for computation

Choose remaining display options

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A riddle (sans funny punch line) What is the difference between a

chloropleth map and a 2-D query such as “how many points are in this polygon”?

A fine (boundary) line

In truth, it is a matter of style of output.

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Voronoi (Theissen) polygons – An important type of chloropleth

Each point is “credited” with the region of points closer to it than to any other point

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Dulaunay Triangulation By testing

adjacent regions of the Voronoi diagram, interesting questions can be answered.

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“Voronoi” queries Where is the nearest “facility”, e.g.

fire house, hospital, Denny’s restaurant?

Which is the “second best” facility?

What is the largest empty region (to put new store, or toxic dump)

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Continuous fields

Requires approximating

Often involves slope and aspect

Commonly used for shading maps

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Building “shade” Shaded maps intrinsically include a

“camera” and a “direction”

For “perspective”, color is determined using the dot product of the value of the normal (aspect) and the camera vector (line of sight)

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Some shaded surfaces

Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 192

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Where has all the rainfall gone?

Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 194

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It’s not calculus Much analysis is done through “cellular”

computation

Conway’s game of Life is an example

http://www.bitstorm.org/gameoflife/

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How is it used in GIS?

Image from: Burrough & McDonnell, Principles of Geographic Information Systems, p. 199

CS 128/ES 228 - Lecture 13b 19

More complex models

To compute the irradiance, I, use the following formula

I = [cos0cos + sin0sincos(0-A)]S0

x exp(-T0/ cos0)

where S0 is the exatmospheric solar flux, 0 is the solar zenith angle, etc.

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Conclusions Surface analysis is handy, but

requires Moderately complex database queries,

or Moderately complex mathematics

Fortunately, much of this is “built-in” through wizards (e.g. buffer wizard)

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Final thoughts

There is no pithy thought today